Consider a plane wave with vacuum wavelength \(\lambda _0\)  scattering by a spherical
particle of radius \(r\) , refractive index \( n = \sqrt{\epsilon \mu }\)  embedded in a non-absorbing host medium with refractive index \( n _1= \sqrt{\epsilon _1 \mu _1}\) , where \(\epsilon (\epsilon _1)\)  and
\(\mu (\mu _1)\)  are the relative permittivity and relative permeability of the sphere (host medium).
The scattering and absorption of incident light by the sphere is described by the Mie scattering theory in terms of normalized scattering efficiency \(Q_{sca}\) , absorption efficiency \(Q_{abs}\) , extinction efficiency \(Q_{ext}\)  and mathematically defined as [1]}, [2]}, [3]}, [4]}
\(Q_{sca} = \frac{2}{x^2} {\sum _{\ell =1}^\infty }{(2\ell +1)(| a_\ell |^2 +|b_\ell |^2}),\) 
\(Q_{abs} = \frac{2}{x^2}{\sum _{\ell =1}^\infty }{(2\ell +1)( {\rm Re}{[a_\ell ]}- \vert a_\ell \vert ^2 +\rm Re[b_\ell ]- \vert b_\ell \vert ^2}),\) 
\(Q_{ext} = Q_{abs}+Q_{sca}, \) 
